Session: Monday Morning, May 13

Time: 10:35

The method of empirical orthogonal functions is commonly used in tomography
to select a set of basis vectors to represent variations in the sound-speed
profile. In this method, historical profiles are used to estimate a profile
covariance matrix, and the eigenvectors corresponding to the largest eigenvalues
of the covariance matrix are taken for the basis vectors. These basis vectors
are the most efficient parametrization of the variations in the profile. They
are NOT, however, the parametrization which leads to the most accurate
post-measurement estimate of the profile, because, in a tomographic experiment,
all profile variations cannot be measured with the same accuracy. In this paper,
the set of basis vectors, which will yield the least error in the
post-measurement estimate of the profile, are derived taking into account
measurement resolution and measurement noise. These improved empirical
orthogonal functions are applied to several canonical problems in ocean acoustic
tomography, and the resulting enhancement in estimation accuracy is
demonstrated. [Work supported by ONR.]